Question

In a random sample of 1919 ​people, the mean commute time to work was 34.834.8 minutes and the standard deviation was 7.17.1 minutes. assume the population is normally distributed and use a​ t-distribution to construct a 9999​% confidence interval for the population mean muμ. what is the margin of error of muμ​? interpret the results

Answer 1

Solution: We are given:

x bar=34.8

s = 7.1

n=19

The 99% confidence interval for the population mean is given below:

xbar +-
`t_{(0.01)/(2)}`
`(s)/(√(n))`

34.8 +- 2.878 (
`(7.1)/(√(19))`)

34.8 +- 4.69

[34.8-4.69,34.8+4.69]

[30.11, 39.49]

Therefore the 99% confidence interval for the population mean is:

30.11≤μ≤39.49

The margin of error is 4.69

There is 99% chance that the confidence interval 30.11≤μ≤39.49 contains the true population mean.